CN110658086B - Asphalt pavement load response analysis method considering tension-compression modulus difference - Google Patents

Asphalt pavement load response analysis method considering tension-compression modulus difference Download PDF

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CN110658086B
CN110658086B CN201910819478.XA CN201910819478A CN110658086B CN 110658086 B CN110658086 B CN 110658086B CN 201910819478 A CN201910819478 A CN 201910819478A CN 110658086 B CN110658086 B CN 110658086B
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吕松涛
樊喜雁
夏诚东
张超
王双双
郑健龙
黄拓
潘勤学
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Changsha University of Science and Technology
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    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
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    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
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    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
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Abstract

The invention discloses an asphalt pavement load response analysis method considering tension-compression modulus difference, and particularly relates to the technical field of road engineering, and the method comprises the following specific steps: s1, four-point bending fatigue test considering the tension and compression difference; s2, exploring a tensile-compression strain development rule in the fatigue process; s3, searching a tensile-compression strain increase rule and a dynamic tensile-compression modulus decay rule in the four-point bending fatigue process; s4, comparing the strain and modulus change rules under the tension and compression stress conditions, and analyzing the movement trend of the neutral surface position in the fatigue process of the bending beam; s5, establishing a new method for designing the asphalt pavement structure based on the failure criterion of the material and the structure in the three-dimensional stress state and based on the double-modulus theory. The invention solves the problems that the rigidity and strength parameters of the material designed by the asphalt pavement structure are not unique, the stress state of the material in the test is not matched with the stress state of the material in the pavement structure, the strength criterion of the asphalt pavement design is unreasonable and the like.

Description

Asphalt pavement load response analysis method considering tension-compression modulus difference
Technical Field
The invention relates to the technical field of road engineering, in particular to an asphalt pavement load response analysis method considering tension-compression modulus difference.
Background
After the highway in China has been continuously and rapidly developed for more than twenty years, the development statistical bulletin in of the traffic and transportation industry in 2017 issued by the department of transportation shows that the total highway mileage in China reaches 477 kilometers by the end of the year 2017, wherein the highway mileage is 13.6 kilometers. Second only to the united states, highway mileage has leaped the world first. Therefore, the current asphalt pavement design method guides the construction of about 14 thousands of kilometers of expressways and millions of kilometers of ordinary roads, and makes important contribution to the road traffic development in China.
Transportation is an economic life line of all countries in the world, and roads are used as important components of transportation infrastructure, bear most of transportation tasks of people flow and logistics, and play a vital role in national economic construction and development. However, the construction of highway infrastructure requires large capital investment, consumes large amounts of energy, and emits large amounts of greenhouse gases. The durability of the road infrastructure is improved, the major and medium repair period of the road can be prolonged, the consumption of resources and energy and the emission of greenhouse gases are obviously reduced, and the method has obvious economic benefit and great strategic significance.
The research on road durability countermeasures can provide guarantee for improving the road quality, promoting the service capability and improving the service quality. Frequent maintenance and construction seriously reduce the traffic capacity and the operation efficiency of a road network, greatly increase the construction and maintenance cost of roads, also generate adverse social influence, are difficult to meet the requirements of society on traffic, and how to improve the durability of roads in China becomes an important technical problem to be urgently solved for ensuring the benign development of social traffic.
The Chinese asphalt pavement design method adopts a mechanics-experience method: calculating load response of a pavement structure by a mechanical method, taking homogeneous isotropic line elasticity mechanics as a mechanical model for structural response calculation, and taking elastic modulus as a calculation parameter; the resistance of the pavement structure is determined by an empirical method, and the design standard of the pavement structure is determined by indoor tests, a large amount of field detection and failure state investigation and combination of the strength and the fatigue property of the material. The material parameters adopted by the structural design of the asphalt pavement are as follows: stiffness parameters: modulus of restitution-the mechanical response of the calculated pavement structure. Strength parameters: ultimate strength. Fatigue parameters: structural fatigue strength characteristics. And determining the resistance of each structural layer according to the ultimate strength and structural fatigue strength characteristics.
The existing asphalt pavement design method uses the theory of an elastic layered system to carry out analysis and calculation, and assumes that each layer is completely continuous, homogeneous, isotropic and has tiny displacement and deformation. However, in the actual stress of the asphalt pavement structure, a tensile stress area and a compressive stress area generally exist at the same time, and the strength and the modulus of the pavement material are closely related to the experimental conditions and the stress state, so that the pavement material shows the property of different tensile and compressive moduli. The existing design method simply adopts compression-resistant resilience modulus as a semi-rigid material parameter of the asphalt pavement, so that larger errors exist in the thickness design and stress-strain calculation results;
the rigidity parameters of the materials obtained by different test methods have tension-compression difference, the strength parameters of the materials obtained by different test methods also have tension-compression difference, the non-uniqueness of the material parameters causes the non-uniqueness of the design parameters and the unscientific nature of the design method, the non-uniqueness of the strength and the rigidity parameters is the essential characteristic of the road material, and the measure (establishing the strength model in a three-dimensional stress state) of the non-uniqueness of the strength parameters is solved.
Disclosure of Invention
In order to overcome the defects of the prior art, the embodiment of the invention provides an asphalt pavement load response analysis method considering the difference of tensile modulus and compressive modulus, the invention is based on the failure criterion of materials and structures in a three-dimensional stress state, a new method for designing an asphalt pavement structure is established on the basis of a double-modulus theory, the tensile modulus and the compressive modulus of the materials are obtained through a direct tensile test and a direct compression test, the stress-strain relation of the double-modulus theory is applied to calculate the mechanical response of the structure, and the problems that the material rigidity and the strength parameter of the asphalt pavement structure design are not unique, the stress state in the material test is not matched with the stress state in the pavement structure, the strength criterion of the asphalt pavement structure design is unreasonable and the like are solved.
In order to achieve the purpose, the invention provides the following technical scheme: a bituminous pavement load response analysis method considering tension-compression modulus difference comprises the following specific steps:
s1, a four-point bending fatigue test considering the tension and compression difference;
s2, exploring a tensile-compression strain development rule in the fatigue process; disclosing a tensile and compressive strain increase rule and a dynamic tensile and compressive modulus decay rule in the bending fatigue process, comparing strain and modulus change rules under tensile and compressive stress conditions, and searching characteristic points of the tensile and compressive strain and the dynamic tensile and compressive modulus in the fatigue process, including characteristic values of an initial value, a limit value and a change rate;
s3, searching a tensile-compression strain increase rule and a dynamic tensile-compression modulus decay rule in the four-point bending fatigue process;
s4, comparing the strain and modulus change rules under the tension and compression stress conditions, and analyzing the movement trend of the neutral surface position in the fatigue process of the bending beam;
s5, based on the failure criteria of the material and the structure under the three-dimensional stress state, establishing a new method for designing the asphalt pavement structure based on the double-modulus theory, wherein the calculation process of the double-modulus theory finite element method is as follows:
s5.1, selecting initial parameters, calculating the stress state of each point by using a common finite element method, and generally using the stress state of an elastic layered system as an initial state;
s5.2, calculating an elastic matrix of the unit and a rigidity matrix of the unit according to the stress state of the unit and the double-modulus theory, and assembling to form a total rigidity matrix of the double-modulus theory;
s5.3, calculating node displacement according to the overall stiffness matrix, and calculating the stress state of each unit;
and S5.4, comparing the deviations of the node displacement or the stress obtained by the two calculations before and after the calculation, and if the deviation is greater than a set error, turning to the second step to start the next iterative calculation until the error requirement is met.
In a preferred embodiment, the four-point bending fatigue testing step in step S1 is as follows:
s1.1, preparing a test piece; preparing test pieces by adopting a static pressure forming method, selecting the test pieces with the sizes of 100mm multiplied by 400mm, adopting the compaction degree of 98 percent for each test piece, carrying out curing under the curing condition required by the specification, namely the temperature is 20 +/-2 ℃, the relative humidity is more than or equal to 95 percent, the curing age is 90 days, and the last day of the curing period is saturated with water for 24 hours;
s1.2, performing pretreatment on a test piece; smearing treatment is carried out on the position of the surface of the test piece to be adhered with the strain gauge, and the concrete operation is as follows: a. cement used in the mixture is adopted to prepare cement paste one week before the test, and the cement paste is carefully smeared at the position of adhering a strain gauge on the surface of the test piece; b. polishing the surface of the test piece by using fine sand paper, measuring by using a ruler, drawing a position reference line for adhering the strain gauge on the surface of the test piece, and adhering the strain gauge by taking the reference line as a reference; the strain gauge is adhered to the upper surface and the lower surface of the test piece along the length direction of the test piece, the center of the strain gauge is aligned with the center of the beam span, and the distance between the outer edge of the strain gauge and the edge of the test piece is about 3 cm;
s1.3, performing a four-point bending fatigue test, specifically operating as follows:
a. selecting an MTSLAndmak370.10 multifunctional material test system for testing, selecting different loading devices to be connected on a loading head, and performing four different loading tests of static and dynamic pulling, pressing, bending and shearing on different test pieces; various environments are simulated by adjusting the parameter setting of the environment box, so that the test process is closer to the actual environment;
b. carrying out fatigue test by using a fatigue test load loading mode which is a stress control mode, wherein the loading frequency is 10Hz, the loading waveform of a half sine wave is loaded by selecting loads with four stress intensity ratio levels of 0.8, 0.75, 0.7 and 0.65, and the minimum stress value of the cyclic load is 2% of the maximum stress value;
c. a strain test system is used for collecting strain; in the test, an 1/4 bridge is adopted to measure the strain on the surface of the test piece, namely only one measuring strain gauge is connected to the bridge, and no temperature compensation gauge is arranged; the sampling frequency was 100Hz during the test.
In a preferred embodiment, in step S2, the step of exploring the development law of tensile and compressive strain during fatigue process is as follows:
s2.1, searching for a deformation development rule in the fatigue process; listing test pieces with a certain stress ratio, detecting the rebound strain change values of different periods in the bending-pulling fatigue process under the condition of repeated loading of a hemipositive vector wave, then obtaining a tension-compression strain change rule, carrying out a fatigue test for contrastively analyzing different stress ratio levels, carrying out fatigue life normalization treatment, and obtaining a change rule of the rebound tension-compression strain along with the life ratio N/Nf;
s2.2, determining a damage limit strain value; according to a phase division method in the process of changing strain along with the life ratio, obtaining a linear relation showing good damage limit tension-compression strain and stress ratio according to the limit damage point strain of the fatigue life under different stress levels, the fatigue life of a parallel test piece, the average value of strain limits and the rule that the damage limit of rebound tension-compression strain changes along with the stress, and then respectively carrying out linear fitting on the rebound tension-compression strain and the stress level by using a formula, wherein the formula is as follows:
εmax＝A+Bσ/S
in the formula: epsilonmaxIs a limiting strain value of 10-6(ii) a sigma/S is the stress ratio; A. b is a fitting parameter;
s2.3, determining an initial strain value; and linearly fitting the tension-compression strain and the fatigue times in the stable growth stage by using a formula, wherein the formula is as follows:
ε1＝ε10+kN
ε2＝ε20+kN
in the formula: epsilon1To stabilize the strain in the growth phase, epsilon10Is the initial tensile strain value, ε2To stabilize the compressive strain in the growth phase,. epsilon20Is the value of the initial compressive strain,. epsilon10、ε20The strain is obtained by post-extension in the linear regression process, k is the strain growth rate, and N is the fatigue times;
according to the initial values of the tension-compression strain and the tension-compression rebound strain obtained by linear fitting and the change rule of the initial values of the tension-compression rebound strain along with the stress ratio, obtaining a good linear relation between the initial tension-compression strain and the stress ratio, and then performing linear fitting on the initial values of the tension-compression rebound strain and the stress ratio by using a formula, wherein the formula is as follows:
ε0＝A+Bσ/S
in the formula: epsilon0Is an initial strain value, 10-6; sigma/S is the stress ratio; A. b is a fitting parameter;
s2.4, analyzing the growth rate of the strain stabilization stage; detecting the rebound tensile strain growth rate under different stress ratios to obtain good correlation between the strain growth rate and the stress ratio, and performing exponential growth function fitting on the rebound growth rate and the stress level respectively by using a formula, wherein the formula is as follows:
lg(Vε)＝A+Bσ/S
in the formula: vεIs the rate of strain increase; sigma/S is the stress ratio; A. and B is a fitting parameter.
In a preferred embodiment, in the step S3, the calculation formulas of the layer bottom tensile modulus and the layer top compression modulus in the four-point bending test are respectively shown in the following two formulas:
Figure BDA0002187132940000061
Figure BDA0002187132940000062
s3.1, dividing a modulus decay law into two stages according to the decay laws of the pull-down modulus and the press-down modulus with the service life ratio under different stress ratios;
s3.1.1, determination of initial value of modulus: taking the modulus obtained by testing near the 50 th load cycle as the initial modulus, and taking the average value of the modulus values of 45 th to 50 th cycles as the initial modulus;
s3.1.2, determination of destruction limit modulus value: the method comprises the following steps of (1) taking the ultimate failure point modulus values of fatigue life under different stress levels, wherein the data of the ultimate failure point is the original data acquired last time before a test piece is broken in a test, calculating the average value of the fatigue life and the ultimate modulus of a parallel test piece, obtaining a linear relation showing good damage ultimate tensile and compressive modulus and stress ratio, and respectively carrying out linear fitting on the damage ultimate tensile and compressive modulus and the stress levels by using a formula, wherein the formula is as follows:
Emin＝A+Bσ/S
in the formula: eminIs the ultimate strain value, MPa; sigma/S is the stress ratio; A. b is a fitting parameter;
s3.1.3, establishment of a modulus decay model: the dynamic modulus decay is fitted using a power function related to the cycle life ratio of the following formula:
Figure BDA0002187132940000063
wherein 0<m<1
In the formula: e is the dynamic modulus during fatigue, E0As an initial value of dynamic modulus, EminIs the minimum value of dynamic modulus in fatigue failure, N is the fatigue load cycle number, NfM is the power exponent of the decay law of the modulus for fatigue life;
the above equation can also be expressed as the dynamic modulus power function decay model as follows:
Figure BDA0002187132940000064
and (3) taking m values fitted with the tensile and compressive moduli with different stress ratios, obtaining a change rule of the m values along with the stress ratios, and obtaining a decay rule of the stress level and the dynamic modulus of the cement stabilized macadam along with the decay of the service life ratio.
In a preferred embodiment, in the step S4, a change rule of the neutral plane position of the tension-compression difference with the number of times of loading is analyzed;
the relative position of the neutral plane can be obtained from the following formula:
Figure BDA0002187132940000071
in the formula, H is the relative height of a neutral plane, the beam bottom is 0, the beam top is 1, H1Is the height of the tension zone, h is the total height of the beam;
s4.1, dividing the position change rule of the neutral surface into two stages according to the change rule of the relative position of the neutral surface with the service life ratio under the condition of different stress ratios;
s4.2, position of neutral plane in failure: according to a phase dividing method in the process that the neutral surface position changes along with the life ratio, the relative position of the neutral surface of a limit failure point of the fatigue life under different stress ratios is obtained, the average value of the fatigue life of the parallel test piece and the neutral surface position during failure is obtained, the rule that the neutral surface position changes along with the stress ratio during failure is obtained, the linear relation that the neutral surface position and the stress ratio present good during failure is obtained, a formula is used for carrying out linear fitting on the relative position and the stress ratio of the neutral surface, and the formula is as follows:
Hmax＝A+Bσ/S
in the formula: hmaxRelative position of neutral plane in damage; sigma/S is the stress ratio; A. b is a fitting parameter;
s4.3, determining the initial position of the neutral plane: according to the rule that the position of the neutral surface changes along with the stress ratio, linear fitting is carried out on the relative position of the neutral surface and the fatigue times in the stable growth stage by using a formula, wherein the formula is as follows:
H＝H0+kN
in the formula: h0The initial value of the relative position of the neutral plane is obtained by the backward delay in the linear regression process, k is the strain growth rate, and N is the fatigue times;
obtaining the initial relative position of the neutral surface under different stress ratios according to linear fitting, obtaining the change of the initial value of the relative position of the neutral surface along with the stress ratio, obtaining the good linear relation between the initial value of the relative position of the neutral surface and the stress ratio, and performing linear fitting on the initial value of the relative position of the neutral surface and the stress ratio by using a formula, wherein the formula is as follows:
H0＝A+Bσ
in the formula: h0The relative position initial value of the neutral plane is obtained; sigma/S is the stress ratio; A. b is a fitting parameter;
s4.4, analyzing the growth rate of the relative position of the neutral plane in a stable stage; taking the position change rate of the neutral surface under different stress ratios to obtain the change rule of the position change rate of the neutral surface along with the stress, obtaining the good correlation between the relative position increase rate of the neutral surface and the stress ratio, and performing exponential growth function fitting on the relative position increase rate of the neutral surface and the stress ratio by using a formula, wherein the formula is as follows:
lg(V)＝A+Bσ/S
in the formula: v is the relative position growth rate of the neutral plane; sigma/S is the stress ratio; A. and B is a fitting parameter.
In a preferred embodiment, in the step S5,
unit stiffness matrix [ K ]e]The formula is as follows:
Figure BDA0002187132940000081
Figure BDA0002187132940000082
the cell stiffness matrix [ K ] is formulated as follows: [K] { u } ═ F }
Where { u } is the node displacement column vector, { F } is the node force column vector;
the bi-modal theory differs in the stiffness matrix, which is inherently a difference in the elastic matrix.
In a preferred embodiment, in the step S5,
the elastic matrix formula in the principal stress coordinate system is as follows:
{σ’}＝[D’]{ε’}
Figure BDA0002187132940000091
Δ＝1-2μαμβμγ-(μαμβ+μβμγ+μγμα)
the elastic matrix formula under an arbitrary coordinate system is as follows:
Figure BDA0002187132940000092
Figure BDA0002187132940000093
Figure BDA0002187132940000094
because of the fact that
Figure BDA0002187132940000095
So [ D ]]＝[Lε]T[D’][Lε]。
In a preferred embodiment, in step S5, the elastic matrix in any coordinate system is characterized as follows: the elastic matrix of the double-modulus theory has no uniqueness; the value of the elastic matrix is influenced by the stress state in a main stress coordinate system, the main stress is tensile, and the corresponding elastic modulus and Poisson ratio are respectively E+And mu+(ii) a Otherwise, respectively taking E-And mu-(ii) a The elastic matrix in any coordinate system is different due to different positions and directions; the ratio of Poisson's ratio to modulus at any position and in any direction is a constant, i.e., μ+/E+＝μ-/E-。
The invention has the technical effects and advantages that:
the invention is based on the failure criterion of materials and structures in a three-dimensional stress state, establishes a new method for designing the asphalt pavement structure based on a double-modulus theory, obtains the tensile modulus and the compressive modulus of the materials through a direct tensile test and a direct compression test, and performs the mechanical response calculation of the structure by applying the stress-strain relationship of the double-modulus theory, thereby solving the problems that the material rigidity and the strength parameters of the asphalt pavement structure design are not unique, the stress state in the material test is not matched with the stress state in the pavement structure, the strength criterion of the asphalt pavement design is unreasonable and the like, remarkably improving the design level and the service life of the asphalt pavement, and effectively reducing the whole life cycle cost of the asphalt pavement.
Drawings
FIG. 1 is a finite element method calculation flow chart based on the dual-mode theory according to the present invention.
FIG. 2 is a one-dimensional stress-strain relationship diagram of the bimodal material of the present invention.
FIG. 3 is a constitutive model diagram in a three-dimensional stress state according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A bituminous pavement load response analysis method considering tension-compression modulus difference comprises the following specific steps:
s1, a four-point bending fatigue test considering the tension and compression difference; the four-point bending fatigue test comprises the following steps:
s1.1, preparing a test piece; preparing test pieces by adopting a static pressure forming method, selecting the test pieces with the sizes of 100mm multiplied by 400mm, adopting the compaction degree of 98 percent for each test piece, carrying out curing under the curing condition required by the specification, namely the temperature is 20 +/-2 ℃, the relative humidity is more than or equal to 95 percent, the curing age is 90 days, and the last day of the curing period is saturated with water for 24 hours;
s1.2, performing pretreatment on a test piece; smearing treatment is carried out on the position of the surface of the test piece to be adhered with the strain gauge, and the concrete operation is as follows: a. cement used in the mixture is adopted to prepare cement paste one week before the test, and the cement paste is carefully smeared at the position where the strain foil is to be pasted on the surface of the test piece; b. polishing the surface of the test piece by using fine sand paper, measuring by using a ruler, drawing a position reference line for adhering the strain gauge on the surface of the test piece, and adhering the strain gauge by taking the reference line as a reference; the strain gauge is adhered to the upper surface and the lower surface of the test piece along the length direction of the test piece, the center of the strain gauge is aligned with the center of the beam span, and the distance between the outer edge of the strain gauge and the edge of the test piece is about 3 cm;
s1.3, performing a four-point bending fatigue test, specifically operating as follows:
a. selecting an MTSLAndmak370.10 multifunctional material test system for testing, selecting different loading devices to be connected on a loading head, and performing four different loading tests of static and dynamic pulling, pressing, bending and shearing on different test pieces; various environments are simulated by adjusting the parameter setting of the environment box, so that the test process is closer to the actual environment;
b. carrying out fatigue test by using a fatigue test load loading mode which is a stress control mode, wherein the loading frequency is 10Hz, the loading waveform of a half sine wave is loaded by selecting loads with four stress intensity ratio levels of 0.8, 0.75, 0.7 and 0.65, and the minimum stress value of the cyclic load is 2% of the maximum stress value;
c. a strain test system is used for collecting strain; in the test, an 1/4 bridge is adopted to measure the strain on the surface of the test piece, namely only one measuring strain gauge is connected to the bridge, and no temperature compensation gauge is arranged; during the test, the sampling frequency is 100 Hz;
s2, exploring a tensile-compression strain development rule in the fatigue process; disclosing a tensile and compressive strain increase rule and a dynamic tensile and compressive modulus decay rule in the bending fatigue process, comparing strain and modulus change rules under the tensile and compressive stress conditions, and searching characteristic points of the tensile and compressive strain and the dynamic tensile and compressive modulus in the fatigue process, including characteristic values of an initial value, a limit value and a change rate;
the steps for exploring the development rule of the tension-compression strain in the fatigue process are as follows:
s2.1, searching for a deformation development rule in the fatigue process; listing test pieces with a certain stress ratio, detecting the rebound strain change values of different periods in the bending-pulling fatigue process under the condition of repeated loading of a hemipositive vector wave, then obtaining a tension-compression strain change rule, carrying out a fatigue test for contrastively analyzing different stress ratio levels, carrying out fatigue life normalization treatment, and obtaining a change rule of the rebound tension-compression strain along with the life ratio N/Nf;
s2.2, determining a damage limit strain value; according to a phase division method in the process of changing strain along with the life ratio, obtaining a linear relation showing good damage limit tension-compression strain and stress ratio according to the limit damage point strain of the fatigue life under different stress levels, the fatigue life of a parallel test piece, the average value of strain limits and the rule that the damage limit of rebound tension-compression strain changes along with the stress, and then respectively carrying out linear fitting on the rebound tension-compression strain and the stress level by using a formula, wherein the formula is as follows:
εmax＝A+Bσ/S
in the formula: epsilonmaxIs a limiting strain value of 10-6(ii) a sigma/S is the stress ratio; A. b is a fitting parameter;
s2.3, determining an initial strain value; and linearly fitting the tension-compression strain and the fatigue times in the stable growth stage by using a formula, wherein the formula is as follows:
ε1＝ε10+kN
ε2＝ε20+kN
in the formula: epsilon1To stabilize the strain in the growth phase, epsilon10Is the initial tensile strain value, epsilon2To stabilize the compressive strain in the growth phase,. epsilon20Is the value of the initial compressive strain,. epsilon10、ε20The strain is obtained by post-extension in the linear regression process, k is the strain growth rate, and N is the fatigue times;
according to the initial values of the tension-compression strain and the tension-compression rebound strain obtained by linear fitting and the change rule of the initial values of the tension-compression rebound strain along with the stress ratio, obtaining a good linear relation between the initial tension-compression strain and the stress ratio, and then performing linear fitting on the initial values of the tension-compression rebound strain and the stress ratio by using a formula, wherein the formula is as follows:
ε0＝A+Bσ/S
in the formula: epsilon0Is an initial strain value, 10-6; sigma/S is the stress ratio; A. b is a fitting parameter;
s2.4, analyzing the growth rate of the strain stabilization stage; detecting the rebound tensile strain growth rate under different stress ratios to obtain good correlation between the strain growth rate and the stress ratio, and performing exponential growth function fitting on the rebound growth rate and the stress level respectively by using a formula, wherein the formula is as follows:
lg(Vε)＝A+Bσ/S
in the formula: vεIs the strain growth rate; sigma/S is the stress ratio; A. b is a fitting parameter;
s3, searching a tensile-compression strain increase rule and a dynamic tensile-compression modulus decay rule in the four-point bending fatigue process; the calculation formulas of the layer bottom tensile modulus and the layer top compression modulus of the four-point bending test are respectively shown as the following two formulas:
Figure BDA0002187132940000121
Figure BDA0002187132940000131
s3.1, dividing a modulus decay law into two stages according to the decay laws of the pull-down modulus and the press-down modulus with the service life ratio under different stress ratios;
s3.1.1, determination of initial value of modulus: taking the modulus obtained by testing near the 50 th load cycle as the initial modulus, and taking the average value of the modulus values of 45 th to 50 th cycles as the initial modulus;
s3.1.2, determination of destruction limit modulus value: the method comprises the following steps of (1) taking the ultimate failure point modulus values of fatigue life under different stress levels, wherein the data of the ultimate failure point is the original data acquired last time before a test piece is broken in a test, calculating the average value of the fatigue life and the ultimate modulus of a parallel test piece, obtaining a linear relation showing good damage ultimate tensile and compressive modulus and stress ratio, and respectively carrying out linear fitting on the damage ultimate tensile and compressive modulus and the stress levels by using a formula, wherein the formula is as follows:
Emin＝A+Bσ/S
in the formula: eminIs the ultimate strain value, MPa; sigma/SIs the stress ratio; A. b is a fitting parameter;
s3.1.3, establishment of a modulus decay model: the dynamic modulus decay is fitted using a power function related to the cycle life ratio of the following formula:
Figure BDA0002187132940000132
wherein 0<m<1
In the formula: e is the dynamic modulus during fatigue, E0As an initial value of dynamic modulus, EminIs the minimum value of dynamic modulus in fatigue failure, N is the fatigue load cycle number, NfM is the power exponent of the decay law of the modulus for fatigue life;
the above equation can also be expressed as the dynamic modulus power function decay model as follows:
Figure BDA0002187132940000133
taking m values fitted with different stress ratio tension-compression moduli, obtaining a change rule of the m values along with the stress ratio, and obtaining a decay rule of the stress level and the dynamic modulus of the cement stabilized macadam along with the decay of the service life ratio;
s4, comparing the strain and modulus change rules under the tension and compression stress conditions, and analyzing the movement trend of the neutral surface position in the fatigue process of the bending beam; analyzing the change rule of the neutral surface position of the tension-compression difference along with the loading times;
the relative position of the neutral plane can be obtained from the following formula:
Figure BDA0002187132940000141
in the formula, H is the relative height of a neutral plane, the beam bottom is 0, the beam top is 1, H1Is the height of the tension zone, h is the total height of the beam;
s4.1, dividing the position change rule of the neutral surface into two stages according to the change rule of the relative position of the neutral surface with the service life ratio under the condition of different stress ratios;
s4.2, position of a neutral plane in damage: according to a phase division method in the process that the neutral surface position changes along with the life ratio, the relative position of the neutral surface of the limit damage point of the fatigue life under different stress ratios is obtained, the average value of the fatigue life of the parallel test piece and the neutral surface position during damage is obtained, the rule that the neutral surface position changes along with the stress ratio during damage is obtained, the linear relation that the neutral surface position and the stress ratio show good during damage is obtained, and the formula is used for carrying out linear fitting on the relative position and the stress ratio of the neutral surface, and is as follows:
Hmax＝A+Bσ/S
in the formula: hmaxRelative position of neutral plane in damage; sigma/S is the stress ratio; A. b is a fitting parameter;
s4.3, determining the initial position of the neutral plane: according to the rule that the position of the neutral surface changes along with the stress ratio, linear fitting is carried out on the relative position of the neutral surface and the fatigue times in the stable growth stage by using a formula, wherein the formula is as follows:
H＝H0+kN
in the formula: h0The initial value of the relative position of the neutral plane is obtained by the backward delay in the linear regression process, k is the strain growth rate, and N is the fatigue times;
obtaining the initial relative position of the neutral surface under different stress ratios according to linear fitting, obtaining the change of the initial value of the relative position of the neutral surface along with the stress ratio, obtaining the good linear relation between the initial value of the relative position of the neutral surface and the stress ratio, and performing linear fitting on the initial value of the relative position of the neutral surface and the stress ratio by using a formula, wherein the formula is as follows:
H0＝A+Bσ
in the formula: h0The relative position initial value of the neutral plane is obtained; sigma/S is the stress ratio; A. b is a fitting parameter;
s4.4, analyzing the growth rate of the relative position of the neutral plane in a stable stage; taking the position change rate of the neutral surface under different stress ratios to obtain the change rule of the position change rate of the neutral surface along with the stress, obtaining the good correlation between the relative position increase rate of the neutral surface and the stress ratio, and performing exponential growth function fitting on the relative position increase rate of the neutral surface and the stress ratio by using a formula, wherein the formula is as follows:
lg(V)＝A+Bσ/S
in the formula: v is the relative position growth rate of the neutral plane; sigma/S is the stress ratio; A. b is a fitting parameter;
s5, establishing a new method for designing the asphalt pavement structure based on the failure criterion of the material and the structure in the three-dimensional stress state and based on the double-modulus theory;
basic assumption of the double-modulus theory:
the material is a continuous homogeneous isotropic linear elastomer, but shows different elastic properties due to different signs of main stress; the deformation of the material has the characteristic of small deformation, namely, high-order small quantity is ignored in a geometric equation, and only a linear deformation part is considered; in a main stress coordinate system, the elastic modulus and the Poisson ratio change along with the sign of the main stress; compliance matrix symmetry hypothesis mu+/E+＝μ-/E-；
Constitutive model in one-dimensional stress state (fig. 2):
Figure BDA0002187132940000151
E+≠E-
μ+/E+＝μ-/E-
constitutive model under three-dimensional stress state:
(1) constitutive equations in the principal stress coordinate system;
Figure BDA0002187132940000161
μα/Eα＝μβ/Eβ＝μγ/Eγ
the constitutive equation of the double-modulus theory is established in a principal stress coordinate system; the magnitude and sign of stress strain in the principal stress coordinate system are uniquely determined; the stress strain and sign in the non-principal stress coordinate system are varied; eα，Eβ，EγTaking E according to the signs of the principal stresses+Or E-；
(2) The conversion relation between stress strain and main stress and main strain under a coordinate system in any direction;
[σ’]＝[L]{σ}[LT] [ε’]＝[L]{ε}[LT]
wherein, [ sigma']＝(σασβσγ)TIs the principal stress column vector; [ epsilon']＝(εαεβεγ)TIs the principal strain column vector;
{σ}＝(σxσyσzτxyτyzτzx)Tis an arbitrary stress column vector; { e } - ((e) })xεyεzγxyγyzγzx)TIs an arbitrary strain column vector;
[σ’]＝[Lσ]{σ} [ε’]＝[Lε]{ε}
Figure BDA0002187132940000162
Figure BDA0002187132940000163
Figure BDA0002187132940000164
direction cosine between principal stress coordinate and arbitrary specified coordinate:
Figure BDA0002187132940000171
(3) constitutive equation under non-principal stress coordinate system:
Figure BDA0002187132940000172
Figure BDA0002187132940000173
Figure BDA0002187132940000174
Figure BDA0002187132940000175
elastic constant of bimodal theory:
independent elastic constants: tensile modulus E+Amount of pressing E-Ratio of Poisson's ratio to modulus μ+/E+＝μ-/E-＝const；
Dependent elastic constants: shear modulus G, bulk modulus K: all the components change along with the tension-compression modulus, the tension-compression Poisson's ratio and the main stress state;
a double-modulus theoretical elastic modulus test method comprises the following steps:
common modulus testing methods include direct tensile, direct compression, bend tensile and indirect tensile tests; the parameters of the materials obtained by different test methods are different, and the parameters are artificially selected; the direct tensile and direct compression tests are methods for testing the good elastic modulus of the material, and the full section is equal stress during the test; the bending and stretching test and the indirect stretching test are actually simple structural tests, and the stress distribution on the section is not uniform during the test;
finite element method of linear elastic theory:
unit stiffness matrix [ K ]e]The formula is as follows:
Figure BDA0002187132940000181
Figure BDA0002187132940000182
the cell stiffness matrix [ K ] is formulated as follows: [K] { u } ═ F }
Where { u } is the node displacement column vector, { F } is the node force column vector;
the difference of the double-modulus theory lies in the rigidity matrix, the essence of which is the difference of the elastic matrix;
(1) the elastic matrix formula in the principal stress coordinate system is as follows:
{σ’}＝[D’]{ε’}
Figure BDA0002187132940000183
Δ＝1-2μαμβμγ-(μαμβ+μβμγ+μγμα)
(2) the elastic matrix formula under an arbitrary coordinate system is as follows:
Figure BDA0002187132940000184
Figure BDA0002187132940000185
Figure BDA0002187132940000191
because of the fact that
Figure BDA0002187132940000192
So [ D ]]＝[Lε]T[D’][Lε]
(4) The elastic matrix in an arbitrary coordinate system is characterized as follows:
the elastic matrix of the double-modulus theory has no uniqueness;
the value of the elastic matrix is influenced by the stress state in the principal stress coordinate systemThe principal stress is tensile, and the corresponding elastic modulus and Poisson's ratio are respectively E+And mu+(ii) a Otherwise, respectively take E-And mu-；
The elastic matrix in any coordinate system is different due to different positions and directions;
the ratio of Poisson's ratio to modulus at any position and in any direction is a constant, i.e., μ+/E+＝μ-/E-。
The calculation process of the double-modulus theoretical finite element method is as follows:
s5.1, selecting initial parameters, calculating the stress state of each point by using a common finite element method, and generally using the stress state of an elastic layered system as an initial state;
s5.2, calculating an elastic matrix of the unit and a rigidity matrix of the unit according to the stress state of the unit and the double-modulus theory, and assembling to form a total rigidity matrix of the double-modulus theory;
s5.3, calculating node displacement according to the overall stiffness matrix, and calculating the stress state of each unit;
and S5.4, comparing the deviations of the node displacement or the stress obtained by the two calculations before and after the calculation, if the deviation is greater than a set error, turning to the second step to start the next iterative calculation until the error requirement is met, and particularly referring to fig. 1.
And finally: the above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that are within the spirit and principle of the present invention are intended to be included in the scope of the present invention.

Claims (2)

1. A bituminous pavement load response analysis method considering tension-compression modulus difference is characterized by comprising the following steps: the method comprises the following specific steps:
s1, a four-point bending fatigue test considering the tension and compression difference;
the four-point bending fatigue test in step S1 includes the following steps:
s1.1, preparing a test piece; preparing test pieces by adopting a static pressure forming method, selecting the test pieces with the sizes of 100mm multiplied by 400mm, adopting the compaction degree of 98 percent for each test piece, carrying out curing under the curing condition required by the specification, namely the temperature is 20 +/-2 ℃, the relative humidity is more than or equal to 95 percent, the curing age is 90 days, and the last day of the curing period is saturated with water for 24 hours;
s1.2, performing early-stage treatment on a test piece; smearing treatment is carried out on the position of the surface of the test piece to be adhered with the strain gauge, and the concrete operation is as follows: a. cement used in the mixture is adopted to prepare cement paste one week before the test, and the cement paste is carefully smeared at the position of adhering a strain gauge on the surface of the test piece; b. polishing the surface of the test piece by using fine sand paper, measuring by using a ruler, drawing a position reference line for adhering the strain gauge on the surface of the test piece, and adhering the strain gauge by taking the reference line as a reference; the strain gauge is adhered to the upper surface and the lower surface of the test piece along the length direction of the test piece, the center of the strain gauge is aligned with the center of the beam span, and the distance between the outer edge of the strain gauge and the edge of the test piece is about 3 cm;
s1.3, performing a four-point bending fatigue test, specifically operating as follows:
a. selecting an MTSLAndmak370.10 multifunctional material test system for testing, selecting different loading devices to be connected on a loading head, and performing four different loading tests of static and dynamic pulling, pressing, bending and shearing on different test pieces; various environments are simulated by adjusting the parameter setting of the environment box, so that the test process is closer to the actual environment;
b. carrying out fatigue test by using a fatigue test load loading mode which is a stress control mode, wherein the loading frequency is 10Hz, the loading waveform of a half sine wave is loaded by selecting loads with four stress intensity ratio levels of 0.8, 0.75, 0.7 and 0.65, and the minimum stress value of the cyclic load is 2% of the maximum stress value;
c. a strain test system is used for collecting strain; in the test, an 1/4 bridge is adopted to measure the strain on the surface of the test piece, namely only one measuring strain gauge is connected to the bridge, and no temperature compensation gauge is arranged; during the test, the sampling frequency is 100 Hz;
s2, exploring a tensile-compression strain development rule in the fatigue process; disclosing a tensile and compressive strain increase rule and a dynamic tensile and compressive modulus decay rule in the bending fatigue process, comparing strain and modulus change rules under the tensile and compressive stress conditions, and searching characteristic points of the tensile and compressive strain and the dynamic tensile and compressive modulus in the fatigue process, including characteristic values of an initial value, a limit value and a change rate;
in step S2, the step of exploring the development law of tensile-compressive strain in the fatigue process is as follows:
s2.1, searching for a deformation development rule in the fatigue process; listing test pieces with a certain stress ratio, detecting the rebound strain change values of different periods in the bending-pulling fatigue process under the condition of repeated loading of a hemipositive vector wave, then obtaining a tension-compression strain change rule, carrying out a fatigue test for contrastively analyzing different stress ratio levels, carrying out fatigue life normalization treatment, and obtaining a change rule of the rebound tension-compression strain along with the life ratio N/Nf;
s2.2, determining a damage limit strain value; according to a phase division method in the process of changing strain along with the life ratio, obtaining a linear relation showing good damage limit tension-compression strain and stress ratio according to the limit damage point strain of the fatigue life under different stress levels, the fatigue life of a parallel test piece, the average value of strain limits and the rule that the damage limit of rebound tension-compression strain changes along with the stress, and then respectively carrying out linear fitting on the rebound tension-compression strain and the stress level by using a formula, wherein the formula is as follows:
εmax＝A1+B1σ/S
in the formula: epsilonmaxIs a limiting strain value of 10-6(ii) a sigma/S is the stress ratio; a. the1、B1Is a fitting parameter;
s2.3, determining an initial strain value; and linearly fitting the tension-compression strain and the fatigue times in the stable growth stage by using a formula, wherein the formula is as follows:
ε1＝ε10+kN
ε2＝ε20+kN
in the formula: epsilon1To stabilize the strain in the growth phase, epsilon10Is the initial tensile strain value, ε2To stabilize the compressive strain in the growth phase,. epsilon20Is the value of the initial compressive strain,. epsilon10、ε20The strain is obtained by post-extension in the linear regression process, k is the strain growth rate, and N is the fatigue times;
according to the initial values of the tension-compression strain and the tension-compression rebound strain obtained by linear fitting and the change rule of the initial values of the tension-compression rebound strain along with the stress ratio, obtaining a good linear relation between the initial tension-compression strain and the stress ratio, and then performing linear fitting on the initial values of the tension-compression rebound strain and the stress ratio by using a formula, wherein the formula is as follows:
ε0＝A2+B2σ/S
in the formula: epsilon0Is an initial strain value, 10-6(ii) a sigma/S is stress ratio; a. the2、B2Is a fitting parameter;
s2.4, analyzing the growth rate of the strain stabilization stage; detecting the rebound tensile strain growth rate under different stress ratios to obtain good correlation between the strain growth rate and the stress ratio, and performing exponential growth function fitting on the rebound growth rate and the stress level respectively by using a formula, wherein the formula is as follows:
lg(Vε)＝A3+B3σ/S
in the formula: vεIs the strain growth rate; sigma/S is the stress ratio; a. the3、B3Is a fitting parameter;
s3, searching a tensile-compression strain increase rule and a dynamic tensile-compression modulus decay rule in the four-point bending fatigue process;
in step S3, the calculation formulas of the layer bottom tensile modulus and the layer top compression modulus in the four-point bending test are respectively shown in the following two formulas:
Figure FDA0003523306980000031
Figure FDA0003523306980000032
s3.1, dividing a modulus decay law into two stages according to the decay laws of the pull-down modulus and the press-down modulus with the service life ratio under different stress ratios;
s3.1.1, determination of initial value of modulus: taking the modulus obtained by testing near the 50 th load cycle as the initial modulus, and taking the average value of the modulus values of 45 th to 50 th cycles as the initial modulus;
s3.1.2, determination of destruction limit modulus value: the method comprises the following steps of taking the ultimate failure point modulus values of fatigue life under different stress levels, wherein data of the ultimate failure point is original data acquired last time before a test piece is broken in a test, calculating the average values of the fatigue life and the ultimate modulus of parallel test pieces, obtaining a linear relation showing a good damage ultimate tensile and compressive modulus and a good stress ratio, and performing linear fitting on the damage ultimate tensile and compressive modulus and the stress levels by using a formula, wherein the formula is as follows:
Emin＝A4+B4σ/S
in the formula: eminIs the ultimate strain value, MPa; sigma/S is the stress ratio; a. the4、B4Is a fitting parameter;
s3.1.3, establishment of a modulus decay model: the dynamic modulus decay is fitted using a power function related to the cycle life ratio of the following formula:
Figure FDA0003523306980000041
wherein 0<m<1
In the formula: e is the dynamic modulus during fatigue, E0Is an initial value of dynamic modulus, E'minIs the minimum value of dynamic modulus in fatigue failure, N is the fatigue number, NfM is the power exponent of the decay law of the modulus for fatigue life;
the above equation can also be expressed as a dynamic modulus power function decay model as follows:
Figure FDA0003523306980000042
taking m values fitted with different stress ratio tension-compression moduli, obtaining a change rule of the m values along with the stress ratio, and obtaining a decay rule of the stress level and the dynamic modulus of the cement stabilized macadam along with the decay of the service life ratio;
s4, comparing the strain and modulus change rules under the tension and compression stress conditions, and analyzing the movement trend of the neutral surface position in the fatigue process of the bending beam;
in the step S4, the change rule of the neutral surface position of the tension-compression difference along with the number of times of loading is analyzed;
the relative position of the neutral plane can be obtained from the following formula:
Figure FDA0003523306980000043
in the formula, H is the relative height of a neutral plane, the beam bottom is 0, the beam top is 1, H1Is the height of the tension zone, h is the total height of the beam;
s4.1, dividing the position change rule of the neutral surface into two stages according to the change rule of the relative position of the neutral surface with the service life ratio under the condition of different stress ratios;
s4.2, position of neutral plane in failure: according to a phase dividing method in the process that the neutral surface position changes along with the life ratio, the relative position of the neutral surface of a limit failure point of the fatigue life under different stress ratios is obtained, the average value of the fatigue life of the parallel test piece and the neutral surface position during failure is obtained, the rule that the neutral surface position changes along with the stress ratio during failure is obtained, the linear relation that the neutral surface position and the stress ratio present good during failure is obtained, a formula is used for carrying out linear fitting on the relative position and the stress ratio of the neutral surface, and the formula is as follows:
Hmax＝A5+B5σ/S
in the formula: hmaxRelative position of neutral plane in damage; sigma/S is the stress ratio; a. the5、B5Is a fitting parameter;
s4.3, determining the initial position of the neutral plane: according to the rule that the position of the neutral surface changes along with the stress ratio, linear fitting is carried out on the relative position of the neutral surface and the fatigue times in the stable growth stage by using a formula, wherein the formula is as follows:
H＝H0+kN
in the formula: h0The initial value of the relative position of the neutral plane is obtained by the backward delay in the linear regression process, k is the strain growth rate, and N is the fatigue times;
obtaining the initial relative position of the neutral surface under different stress ratios according to linear fitting, obtaining the change of the initial value of the relative position of the neutral surface along with the stress ratio, obtaining the good linear relation between the initial value of the relative position of the neutral surface and the stress ratio, and performing linear fitting on the initial value of the relative position of the neutral surface and the stress ratio by using a formula, wherein the formula is as follows:
H0＝A6+B6σ
in the formula: h0The relative position initial value of the neutral plane is obtained; sigma/S is the stress ratio; a. the6、B6Is a fitting parameter;
s4.4, analyzing the growth rate of the relative position of the neutral plane in a stable stage; taking the position change rate of the neutral surface under different stress ratios to obtain the change rule of the position change rate of the neutral surface along with the stress, obtaining the good correlation between the relative position increase rate of the neutral surface and the stress ratio, and performing exponential growth function fitting on the relative position increase rate of the neutral surface and the stress ratio by using a formula, wherein the formula is as follows:
lg(V)＝A7+B7σ/S
in the formula: v is the relative position growth rate of the neutral plane; sigma/S is the stress ratio; a. the7、B7Is a fitting parameter;
s5, based on the failure criteria of the material and the structure under the three-dimensional stress state, establishing a new method for designing the asphalt pavement structure based on the double-modulus theory, wherein the calculation process of the double-modulus theory finite element method is as follows:
s5.1, selecting initial parameters, calculating the stress state of each point by using a common finite element method, and taking the stress state of an elastic layered system as an initial state;
s5.2, calculating an elastic matrix of the unit and a rigidity matrix of the unit according to the stress state of the unit and the double-modulus theory, and assembling to form a total rigidity matrix of the double-modulus theory;
s5.3, calculating node displacement according to the overall stiffness matrix, and calculating the stress state of each unit;
and S5.4, comparing the deviations of the node displacement or the stress obtained by the two calculations before and after the calculation, and if the deviation is greater than a set error, turning to the second step to start the next iterative calculation until the error requirement is met.
2. The method for analyzing the load response of the asphalt pavement considering the difference of the tensile modulus and the compressive modulus as claimed in claim 1, wherein the method comprises the following steps: in step S5, the elastic matrix in any coordinate system has the following characteristics: the elastic matrix of the double-modulus theory has no uniqueness; the value of the elastic matrix is influenced by the stress state in a main stress coordinate system, the main stress is tensile, and the corresponding elastic modulus and Poisson ratio are respectively E+And mu+(ii) a When the main stress is compression, the corresponding elastic modulus and Poisson's ratio are respectively E-And mu-(ii) a The elastic matrix in any coordinate system is different due to different positions and directions; the ratio of Poisson's ratio to modulus at any position and in any direction is a constant, i.e., μ+/E+＝μ-/E-。
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